# Free modular lattice on 3 generators in Sage

Is there an easy/quick way to obtain the free modular lattice on 3 generators in Sage (it has 28 elements)? I searched a bit but was not able to find a good way. See https://blogs.ams.org/visualinsight/2... for the definition/visualization.

By the way, is there a reference for what the free modular lattice on 2 generators is? I have a guess but I am not sure. Is the poset of join-irreducible elements of the free modular lattice on 3 generators a special poset? Does it have a name?

Well, you could just use the picture, number the vertices and enter the poset by hand.